Strip is rolled with the objective of avoiding strip waviness and of ensuring that the residual stresses over the width of the rolled strip are low in the longitudinal direction. Recently, different rolling adjusters have been used selectively for this purpose for adjusting the gap between the finishing rolls. Examples of such adjusters include, roller reverse bending equipment, intermediate rollers with symmetrically or asymmetrically shaped roller barrels and movable in the axial direction, movable working rollers, equipment for tilting the rollers, as well as the influencing of the thermal profile of the rollers by the action of defined local cooling agents and profile-changeable supporting rollers. For 20-roller rolling mill, the supporting saddles of the outer supporting rollers additionally are used to adjust the gap between the finishing rolls. (H. Galla, H. Jung: "Walzen yon Flachprodukten" (Rolling Flat Products), published by the Deutsche Gesellschaft fuer Metallkunde, Informationsgesellschaft in 1986).
Additional measuring equipment is used in modern rolling mills for determining the course of the longitudinal stresses over the width of the strip to be able to use these adjusters meaningfully to control the profile of the gap between the finishing rolls with the objective of producing strip with low residual stresses in the longitudinal direction. This measuring equipment determines the course of the strip tension such as by special measuring rollers, feelers and/or through the effect of electromagnetic forces.
From the measured course of the strip tension .sigma..sub.li, by eliminating the longitudinal tension .sigma..sub.l externally applied during the rolling (for example, by the reel tension), the course of the residual stress .DELTA..sigma..sub.l,i in the stress-relieved strip EQU .DELTA..sigma.L, i=.sigma.L, i-.sigma.L (1)
can be determined from the measured course of the strip stress
+inherent compressive strains PA1 -inherent tensile strains
and the longitudinal elongation and contraction contributions can be determined from Hooke's law ##EQU1## (see FIG. 1).
The objective pursued is the adjustment of the gap between the finishing rolls by means of the aforementioned adjusters with the help of the signals constantly obtained from the measurement equipment, so that strip waviness is avoided and a strip is produced with a low residual stress in the longitudinal direction.
Special transfer functions are required for the correct conversion of the measured strip tension values .DELTA..sigma..sub.l,i or the longitudinal extension and contraction values into the adjusting values .DELTA.S.sub.i required for correcting the gap between the finishing rolls.
In this connection, it was assumed that, in the absence of or in the presence of only slight lateral flow of the strip during the reduction pass, there is a proportionality between the .DELTA..epsilon..sub.l,i values and the thickness profiles of the deformation values .DELTA..epsilon..sub.h,i derived from the strip running in and out according to EQU .DELTA..epsilon.L, i=.DELTA..epsilon.h, i (3)
and consequently the thickness adjustment values can be derived from the measured .DELTA..epsilon..sub.l,i values.
Moreover, FIG. 2 is EQU .DELTA..epsilon.h, i=.epsilon.h, i -.epsilon. (4)
wherein ##EQU2## wherein ##EQU3##
However, practical rolling experience has shown that the thickness adjusting values .DELTA.S.sub.i, determined for the reduction of the longitudinal stresses from the measured longitudinal extension and stretching values .DELTA..epsilon..sub.l,i using equation (3), do not lead to the aimed-for objective. Special investigations (Bernsmann, G.P.; Iron and Steel Engineer, 1972/3, pages 67-71; Becker, H. & P. Freundel, Wiss. Zeitschrift der TU Magdeburg 19, 1975, vol. 7/8, pages 753-761; Koepstein, E., G.G. Grigorjan, Ju. D. Zeleznow, Neue Huette 1975, 4, pages 226-228), with inclusion of the strip profile running in and out, revealed very large and highly scattered deviations, K.sub.M which were introduced as the correction factor in the equation EQU .DELTA..sigma.L, i=K.sub.M.E (.epsilon.h,i-.epsilon.) (7)
(Equation (7) is related to Equation (3) in the same way as is Equation (2)).
These correction factors include values ranging from K.sub.M =0.05 ... 0.1 ... 0.2. Likewise, it was observed that the longitudinal stress values (.DELTA..sigma..sub.l,i).sub.gem, measured with the strip stress measuring equipment, are much lower than the longitudinal stress changes (.DELTA..sigma..sub.h,i).sub.ber calculated from the thickness profiles. According to Koepstein, this difference is ##EQU4##
It was not possible to identify a dependence of these highly fluctuating correction factors on the characterizing rolling conditions. For this reason, the determination of the adjusting values .DELTA.S.sub.i, required for adjusting the gap between the finishing rolls, from the .DELTA..sigma..sub.l,i and .DELTA..epsilon..sub.l,i values obtained from the strip stress measuring equipment, is subject to very large uncertainties and inaccuracies, so that the rolling of low-residual-stress strip creates considerable problems. The quality deficiencies of the rolled strip resulting therefrom decrease the use value of the rolled strip and result in economic losses.